US9019061B2

US9019061B2 - Magnetic device formed with U-shaped core pieces and power converter employing the same

Info

Publication number: US9019061B2
Application number: US12/751,650
Authority: US
Inventors: Sriram Chandrasekaran
Original assignee: Power Systems Technologies Ltd
Current assignee: Power Systems Technologies Ltd
Priority date: 2009-03-31
Filing date: 2010-03-31
Publication date: 2015-04-28
Also published as: CN102356438B; CN102356438A; US20100254168A1; WO2010114914A1

Abstract

A magnetic device formed with U-shaped core pieces employable in a power converter, and a method of forming the same. In one embodiment, the magnetic device includes a rectilinear core piece formed of a magnetic material, and first and second U-shaped core pieces positioned on the rectilinear core piece. The magnetic device also includes first and second conductive windings formed about the first and second U-shaped core pieces, respectively.

Description

This application claims the benefit of U.S. Provisional Application No. 61/165,184, entitled “Magnetic Device Formed With U-Shaped Core Pieces and Power Converter Employing The Same,” filed on Mar. 31, 2009, which application is incorporated herein by reference.

TECHNICAL FIELD

The present invention is directed, in general, to power electronics and, more specifically, to a magnetic device employable in a power converter.

BACKGROUND

A switched-mode power converter (also referred to as a “power converter” or “regulator”) is a power supply or power processing circuit that converts an input voltage waveform into a specified output voltage waveform. DC-DC power converters convert a direct current (“dc”) input voltage into a dc output voltage. Controllers associated with the power converters manage an operation thereof by controlling the conduction periods of power switches employed therein. Generally, the controllers are coupled between an input and output of the power converter in a feedback loop configuration (also referred to as a “control loop” or “closed control loop”).

To produce a dc output voltage, power converters employ magnetic devices such as inductors and transformers. A high-frequency alternating current (“ac”) voltage is applied to a winding of the magnetic device that is typically converted to another voltage level by an inductive action of the magnetic device. The converted voltage level is rectified by a diode or an active semiconductor device to produce the dc output voltage.

To produce a high level of power conversion efficiency, magnetic devices are often formed with windings wound in a single layer to reduce the proximity effect produced by high-frequency currents flowing in a proximate winding turn. The proximity effect causes high-frequency currents to flow predominantly in only a portion of a conductive winding, thereby increasing the effective resistance of the winding.

Magnetic devices are conventionally constructed with rectilinear core pieces such as “E” and “I” core pieces employed to form a high-frequency transformer or inductor. From practical manufacturing considerations, such designs require that a single-layer winding be formed on the vertical walls of the “E” portion of the magnetic core. Designs with such winding structures do not utilize the horizontal walls of the “E” or the “I” core pieces of the magnetic core, and accordingly introduce a high level of power losses.

Accordingly, what is needed in the art is a physical structure for a magnetic device and related method that provides a configuration to enable a wider distribution of winding turns to avoid the deficiencies in the prior art.

SUMMARY OF THE INVENTION

These and other problems are generally solved or circumvented, and technical advantages are generally achieved, by advantageous embodiments of the present invention, including a magnetic device formed with U-shaped core pieces employable in a power converter, and a method of forming the same. In one embodiment, the magnetic device includes a rectilinear core piece formed of a magnetic material, and first and second U-shaped core pieces positioned on the rectilinear core piece. The magnetic device also includes first and second conductive windings formed about the first and second U-shaped core pieces, respectively.

The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter, which form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and specific embodiment disclosed may be readily utilized as a basis for modifying or designing other structures or processes for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates a block diagram of an embodiment of a power converter constructed according to the principles of the present invention;

FIGS. 2 to 4 illustrate schematic diagrams of exemplary power trains employable in a power converter constructed according to the principles of the present invention; and

FIGS. 5 to 9 illustrate diagrams of embodiments of magnetic devices constructed according to the principles of the present invention.

Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated, and may not be redescribed in the interest of brevity after the first instance. The FIGUREs are drawn to illustrate the relevant aspects of exemplary embodiments.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The making and using of the present exemplary embodiments are discussed in detail below. It should be appreciated, however, that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the invention, and do not limit the scope of the invention.

The present invention will be described with respect to exemplary embodiments in a specific context, namely, a magnetic device including a U-shaped core piece, and a method of forming the same. The magnetic device including a U-shaped core piece provides improved power conversion efficiency by accommodating a larger physical space for turns of a single-layer winding of a conductive material formed thereabout. While the principles of the present invention will be described in the environment of a magnetic device for a power converter, any application that may benefit from a magnetic device such as a power amplifier or a motor controller is well within the broad scope of the present invention.

Referring initially to FIG. 1, illustrated is a block diagram of an embodiment of a power converter including a magnetic device constructed according to the principles of the present invention. The power converter is coupled to a source of electrical power such as an ac mains represented by the ac power source providing an input voltage V_in. The power converter includes a power train 105 that is controlled by a controller 110. The controller 110 generally measures an operating characteristic of the power converter such as an output voltage V_cand controls a duty cycle D of one or more power switches therein in response to the measured operating characteristic to regulate the characteristic. The power converter may form a section of a power supply and provide power to another subsystem thereof, such as an isolating dc-dc power converter coupled to an output thereof that provides a regulated voltage to a load. The power train 105 may employ a boost topology as described herein. The power train 105 of the power converter includes a plurality of power switches coupled to a magnetic device to provide the power conversion function.

Turning now to FIG. 2, illustrated is a schematic diagram of an exemplary power train (including a boost topology) 201 employable in a power converter constructed according to the principles of the present invention. The power train 201 of the power converter receives an input voltage V_in(e.g., an unregulated ac input voltage) from a source of electrical power such as ac mains at an input thereof and provides a regulated output voltage V_Cat

output terminals

205, 206 of the power converter. In keeping with the principles of a boost topology, the output voltage V_Cis generally higher than the input voltage V_insuch that a switching operation thereof can regulate the output voltage V_C. A main power switch S₁, (e.g., an N-channel metal-oxide semiconductor (“NMOS”) active switch or switch) is enabled to conduct by a gate drive signal GD for a primary interval and couples the input voltage V_inthrough a rectifier bridge 203 to a boost inductor L_boost. During a primary interval D, an input current i_inincreases and flows through the boost inductor L_boostto local circuit ground. The boost inductor L_boostis generally formed with a single-layer winding to reduce the proximity effect to increase the efficiency of the power converter.

The duty cycle for the power train 201 depends in steady state on the ratio of the input and output voltages V_in, V_c, respectively, according to the equation:

D = 1 - \frac{V_{in}}{V_{c}} .

During a complementary interval 1-D, the main power switch S₁is transitioned to a non-conducting state and an auxiliary power switch (e.g., the diode D1) conducts. In an alternative circuit arrangement, the auxiliary power switch D1 may include a second active power switch that is controlled to conduct by a complementary gate drive signal. The auxiliary power switch D1 provides a path to maintain the continuity of the input current i_inflowing through the boost inductor L_boost. During the complementary interval 1-D, the input current i_in, flowing through the boost inductor L_boostdecreases, and may become zero and remain zero for a period of time resulting in a “discontinuous conduction mode” of operation.

During the complementary interval 1-D, the input current i_inflowing through the boost inductor L_boostflows through the diode D1 (i.e., the auxiliary power switch) into an output filter capacitor C. In general, the duty cycle of the main power switch S₁(and the complementary duty cycle of the auxiliary power switch D1) may be adjusted to maintain a regulation of the output voltage V_Cof the power converter. Those skilled in the art understand that conduction periods for the main and auxiliary power switches S₁, D1 may be separated by a small time interval by the use of “snubber” circuit elements (not shown) or by control circuit timing to avoid cross conduction current therebetween, and beneficially to reduce the switching losses associated with the power converter. Circuit and control techniques to avoid cross conduction currents between power switches are well understood in the art and will not be described further in the interest of brevity. The boost inductor L_boostis preferably formed with a single-layer winding as described previously hereinabove to reduce power loss associated with the proximity effect.

Turning now to FIG. 3, illustrated is a schematic diagram of an exemplary power train (including a boost topology) 300 employable in a power converter constructed according to the principles of the present invention. The power train 300 includes a first boost regulator subcircuit including a first boost inductor L_boost1, a first diode D1, and a first power switch S₁that receives a first drive signal GD_S1. The power train 300 includes a second boost regulator subcircuit including a second boost inductor L_boost2, a second diode D2, and a second power switch S₂that receives a second drive signal GD_S2. The first and second boost regulator subcircuits are generally controlled to operate roughly 180 degrees out of phase with respect to each other. Out-of-phase operation of the boost regulator subcircuits provides an interleaving effect that doubles the ripple frequency and reduces the ripple magnitude for the current drawn from a rectifier bridge 303 and hence an ac input current i_in. A similar effect is achieved for the current supplied to the output filter capacitor C. The reduction of switching ripple magnitude in the input current i_inhelps reduce filtering requirements for an input filter (not shown) to reduce undesirable high-frequency components that may be conducted back to a source of electrical power such as an ac mains. Substantial benefits accrue from the interleaving effects between the two boost regulator subcircuits. The first and second boost inductors L_boost1, L_boost2are formed with single-layer windings in a magnetic structure. Remaining circuit elements in FIG. 3 and in following FIGUREs that are similar to those in FIG. 2 and will not be described again in the interest of brevity.

Turning now to FIG. 4, illustrated is a schematic diagram of an exemplary power train employable in a power converter constructed according to the principles of the present invention. More specifically, the power train employs a boost topology with two interleaved boost regulator subcircuits and a boost inductor L_boostformed by a magnetic device. The magnetic device includes a common conductive winding or winding N_C(coupled between

terminals

1 and 2 of the magnetic device), a first conductive winding or winding N_S1(coupled between terminals 2 and 3), and a second conductive winding or winding N_S2(coupled between terminals 2 and 4). The first and second windings N_S1, N_S2are electrically and magnetically coupled to the common winding N_C. In an exemplary embodiment, the first and second windings N_S1, N_S2have equal numbers of turns and will hereinafter be represented with a reference symbol N_S. Dots are illustrated in FIG. 4 adjacent to the windings to indicate the sense of each winding (i.e., the winding direction and the sense of the magnetically induced voltage therein).

In an exemplary embodiment, the interleaved boost regulator subcircuits are controlled by a control circuit or controller (not shown) to provide an input current with high-power factor. One boost regulator subcircuit includes a first diode D1 and a first power switch S₁, and a portion of the magnetic device that includes the common winding N_cand the first winding N_S1. The other boost regulator subcircuit includes a second diode D2 and a second power switch S₂, and a portion of the magnetic device that includes the common winding N_cand the second winding N_S2. The output currents i₁, i₂from the boost regulator subcircuits of the power train are interleaved and flow through the first and second diodes D1, D2, respectively, into an output filter capacitor C. Similarly, the input currents to the boost regulator subcircuits are interleaved and form the input current i_in, through the common winding N_c. The first and second power switches S₁, S₂are controlled by first and second control signals GD_S, GD_S2, respectively, to provide duty-cycle control for each of the two interleaved boost regulator subcircuits. The first and second control signals GD_S1, GD_S2may be controlled 180 degrees out of phase with respect to each other, and provide a common duty cycle D for each boost regulator subcircuit. A load, represented by current source 408 is coupled to

output terminals

405, 406 of the power converter and draws an output current i_o.

A common winding N_Cwith selected turns has been described herein as being formed around a center leg of a magnetic core of the magnetic device. In an alternative embodiment, the common winding N_Cwith selected turns may be formed around a common leg of a magnetic core that is not geometrically a center leg. Thus, the terms “center” and “common” as illustrated and used herein with reference to a leg of a magnetic core have a similar meaning, and include a leg of a magnetic core that may not be geometrically located as a center leg.

Turning now to FIG. 5, illustrated is a diagram of an embodiment of a magnetic device constructed according to the principles of the present invention. The magnetic device is a boost inductor L_boostwith rectilinear construction and with single-layer windings. The magnetic device includes the common winding N_cwound around a common leg 505 of the magnetic core, which may be a center leg of the magnetic core, and be electrically and magnetically coupled to first and second windings N_S1, N_S2, each formed in a single layer, and each wound around separate legs (e.g., first and second

outer legs

510, 515, respectively) of the magnetic core. A common flux φ_cflows through the common leg 505 of the magnetic core. First and second fluxes φ₁, φ₂flow through the first and second

outer legs

510, 515, respectively, of the magnetic core. The first and second windings N_S1, N_S2are each conventionally formed as a single layer on the vertical walls of the “E” portion of the magnetic core, which limits the electrical conductivity of these windings.

Terminals

1, 2, 3, and 4 of the magnetic device illustrated in FIG. 5 correspond to terminals similarly numbered and described with reference to FIG. 4. In the embodiment of the magnetic device illustrated in FIG. 5, a gap 520 (e.g., an air gap or a gap of other substantially nonmagnetic material) is formed between an upper surface of the common leg 505 and a lower surface of an upper cross-member 525 of the magnetic core. In an alternative embodiment, gaps, preferably of equal length, can be formed between the upper surfaces of the first and second

outer legs

510, 515 and/or the lower surface of the upper cross-member 525. In further embodiments, gaps, not all necessarily of equal length, can be formed between upper surfaces of all the

legs

505, 510, 515 and the lower surface of the upper cross-member 525. The sense of the winding directions is illustrated by the drawings of the windings N_C, N_S1, N_S2in FIG. 5. Of course, the sense of all the windings N_C, N_S1, N_S2can be reversed to produce the same result, but with magnetic fluxes flowing in opposite directions. In a further alternative embodiment of a magnetic device, the first and second windings N_S1, N_S2can be electrically coupled together external to the magnetic device. In a further alternative embodiment of a magnetic device, the common winding N_Ccan be separated into two winding parts that can be electrically coupled together external to the magnetic device.

Turning now to FIG. 6, illustrated is a diagram of an embodiment of a magnetic device constructed according to the principles of the present invention. The magnetic device includes first and second

U-shaped core pieces

602, 603, separated by a rectilinear core piece or central rectilinear core piece 601 (formed of a magnetic material). The first and second

U-shaped core pieces

602, 603 form a portion of a toroidal core and are preferably formed of high permeability magnetic material, such as a soft ferrite. The conductive windings, such as first and second conductive windings or windings N_s1, N_s2, are each formed about, along substantially the full span or substantially an entire curved length of the first and second

U-shaped core pieces

602, 603, respectively. A third conductive winding or winding (e.g., a common or center conductive winding) N_cis formed about the rectilinear core piece 601, and is electrically coupled to said first and second conductive windings N_s1, N_s2. The magnetic device illustrated herein integrates and couples three inductors into one magnetic device.

Turning now to FIG. 7, illustrated is a diagram of an embodiment of a magnetic device constructed according to the principles of the present invention. The magnetic device includes first and second

U-shaped core pieces

702, 703. The first and second

U-shaped core pieces

702, 703 are now positioned on a common surface of a rectilinear core piece or central rectilinear core piece 701. The first and second

U-shaped core pieces

702, 703 are again preferably formed of high permeability magnetic material, such as a magnetic material with a relative permeability greater than 50. For example, and without limitation, the first and second

U-shaped core pieces

702, 703 may be formed of a soft ferrite. The first and second conductive windings or windings N_s1, N_s2, may each be formed about or along substantially the full span of the first and second

U-shaped core pieces

702, 703, respectively. To simplify the drawing illustrated in FIG. 7, the first and second conductive windings N_s1, N_s2are illustrated spanning only a portion of the first and second

U-shaped core pieces

702, 703, respectively. A third conductive winding or winding (e.g., a common or center conductive winding) N_c, which may be formed as a staple, is again formed about the rectilinear core piece 701.

As indicated illustrated in FIG. 5, the center leg 505 of the magnetic device includes a gap or low-permeability “spacer” 520 in which a substantial portion of the magnetic energy of the magnetic device is stored. In order to reduce mismatch of magnetic flux in the first and second U-shaped core pieces of FIGS. 6 and 7 due to currents flowing in the first and second conductive windings N_s1, N_s2, respectively, gaps may be included in the flux paths of the outer legs formed by the first and second U-shaped core pieces. A gap can be formed, without limitation, of a nonmagnetic material or a magnetic material of low permeability such as air, a plastic material, or a powdered soft ferrite distributed in a nonmagnetic matrix such as a resin or an epoxy.

Turning now to FIG. 8, illustrated is a diagram of an embodiment of a magnetic device constructed according to the principles of the present invention. The magnetic device includes first and second

U-shaped core pieces

802, 803 positioned on a common surface of the rectilinear core piece or central rectilinear core piece 801. First and

second gaps

804, 805, which may be formed of nonmagnetic spacers, are positioned between the first and second

U-shaped core pieces

802, 803, respectively, and the rectilinear core piece 801 to reduce mismatch of magnetic flux in the first and second

U-shaped core pieces

802, 803 due to currents flowing in first and second conductive windings N_s1, N_s2. Again, a third conductive winding or winding (e.g., a common or center conductive winding) N_cis formed about the rectilinear core piece 801.

Turning now to FIG. 9, illustrated is a diagram of an embodiment of a magnetic device constructed according to the principles of the present invention. The magnetic device includes first and second

U-shaped core pieces

902, 903 positioned on a common surface of a rectilinear core piece or central rectilinear core piece 901. The rectilinear core piece 901 is constructed of magnetic material with a distributed gap. In other words, it is constructed of a magnetic material with a lower relative permeability than the relative permeability of the first and second

U-shaped core pieces

902, 903, such as a powdered soft ferrite distributed in a nonmagnetic matrix such as a resin or an epoxy. In this manner, a gap is formed in series with flux flowing in a common or center leg (e.g., the rectilinear core piece 901) of the magnetic structure, as well as gaps formed in series with flux flowing in the outer legs (e.g., the first and second U-shaped core pieces 902, 903). Such use of disparate magnetic materials, such as a higher relative magnetic permeability of the first and second

U-shaped core pieces

902, 903 compared to the relative magnetic permeability of the rectilinear core piece 901, enables construction of a magnetic structure without the need to insert physical spacers to produce series low-permeability gaps, and without the need to accurately shorten the center or common leg of an “E” core piece to produce a series air gap for a flux flowing therein, thereby reducing a manufacturing cost.

Thus, a magnetic device including a U-shaped core piece, and a method of forming the same has been introduced herein. In one embodiment, the magnetic device includes a rectilinear core piece formed of a magnetic material. The rectilinear core piece may be formed with a distributed air gap. The magnetic device also includes first and second U-shaped core pieces formed of a high relative permeability magnetic material and positioned on the rectilinear core piece. The first and second U-shaped core pieces may be positioned on a common surface of the rectilinear core piece, and may form a portion of a toroidal core. A nonmagnetic spacer may be positioned between one of the first and second U-shaped core pieces and a surface of the rectilinear core piece. Typically, a relative permeability of the rectilinear core piece is substantially lower than the relative permeability of the first and second U-shaped core pieces.

The magnetic device also includes first and second conductive windings formed about the first and second U-shaped core pieces, respectively. The first and second conductive windings may be formed over substantially an entire curved length of the first and second U-shaped core pieces, respectively. The magnetic device may also include a third conductive winding (e.g., a common or center conductive winding, or as a staple) formed about the rectilinear core piece, and electrically coupled to the first and second conductive windings.

Those skilled in the art should understand that the previously described embodiments of a power converter including a magnetic device including U-shaped core pieces positioned on a rectilinear core piece and related methods of forming the same are submitted for illustrative purposes only. While a magnetic structure has been described in the environment of a power converter, the magnetic structure may also be applied to other systems such as, without limitation, a power amplifier and a motor controller.

For a better understanding of power converters, see “Modern DC-to-DC Power Switch-mode Power Converter Circuits,” by Rudolph P. Severns and Gordon Bloom, Van Nostrand Reinhold Company, New York, N.Y. (1985) and “Principles of Power Electronics,” by J. G. Kassakian, M. F. Schlecht and G. C. Verghese, Addison-Wesley (1991). The aforementioned references are incorporated herein by reference in their entirety.

Also, although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims. For example, many of the processes discussed above can be implemented in different methodologies and replaced by other processes, or a combination thereof.

Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods, and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present invention, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.

Claims

What is claimed:

1. A magnetic device, comprising:

a rectilinear core piece formed of a magnetic material;

first and second U-shaped core pieces with a bottom surface of ends thereof positioned on a common surface of said rectilinear core piece, a relative permeability of said rectilinear core piece being substantially lower than a relative permeability of said first and second U-shaped core pieces;

first and second conductive windings formed about said first and second U-shaped core pieces, respectively; and

a third conductive winding formed about said rectilinear core piece and electrically coupled to said first and second conductive windings at a common terminal.

2. The magnetic device as recited in claim 1 wherein said first and second conductive windings are formed over substantially an entire curved length of said first and second U-shaped core pieces, respectively.

3. The magnetic device as recited in claim 1 wherein said first and second U-shaped core pieces are formed with a soft ferrite.

4. The magnetic device as recited in claim 1 further comprising a nonmagnetic spacer positioned between said bottom surface of said ends of at least one of said first and second U-shaped core pieces and said common surface of said rectilinear core piece.

5. The magnetic device as recited in claim 1 wherein said first and second U-shaped core pieces are separated by a portion of said common surface of said rectilinear core piece.

6. The magnetic device as recited in claim 1 wherein said third conductive winding is formed as a staple.

7. The magnetic device as recited in claim 1 wherein said first and second conductive windings are formed as a single layer about said first and second U-shaped core pieces, respectively.

8. The magnetic device as recited in claim 1 wherein said rectilinear core piece is formed with a distributed gap.

9. The magnetic device as recited in claim 1 wherein said first and second conductive windings are first and second secondary windings and said third conductive winding is a common winding coupled thereto.

10. The magnetic device as recited in claim 1 wherein said first and the second U-shaped core pieces are each formed as a portion of a toroidal core.

11. A method of forming a magnetic device, comprising:

providing a rectilinear core piece of a magnetic material;

positioning a bottom surface of ends of first and second U-shaped core pieces on a common surface of said rectilinear core piece, a relative permeability of said rectilinear core piece being substantially lower than a relative permeability of said first and second U-shaped core pieces;

forming first and second conductive windings about said first and second U-shaped core pieces, respectively; and

forming a third conductive winding about said rectilinear core piece and electrically coupled to said first and second conductive windings at a common terminal.

12. The method as recited in claim 11 wherein said first and second conductive windings are formed over substantially an entire curved length of said first and second U-shaped core pieces, respectively.

13. The method as recited in claim 11 wherein said first and second U-shaped core pieces formed with a soft ferrite.

14. The method as recited in claim 11 further comprising positioning a nonmagnetic spacer between said bottom surface of said ends of at least one of said first and second U-shaped core pieces and said common surface of said rectilinear core piece.

15. The method as recited in claim 11 wherein said first and second U-shaped core pieces are separated by a portion of said common surface of said rectilinear core piece.

16. The method as recited in claim 11 wherein said third conductive winding is formed as a staple.

17. The method as recited in claim 11 wherein said first and second conductive windings are formed as a single layer about said first and second U-shaped core pieces, respectively.

18. The method as recited in claim 11 wherein said rectilinear core piece is formed with a distributed gap.

19. The method as recited in claim 11 wherein said first and second conductive windings are first and second secondary windings and said third conductive winding is a common winding coupled thereto.

20. The method as recited in claim 11 wherein said first and the second U-shaped core pieces are each formed as a portion of a toroidal core.